In a three-page memorandum submitted to the President, the delegation led by Paswan's son Chirag Paswan raised concerns over "deteriorating" law and order in the state.
"Nowadays political murders and lawlessness are common feature in Bihar," the delegation said, listing some high profile cases, including murder.
The delegation alleged the Bihar police is "deliberately leaving" several loopholes in the Aditya Sachdeva murder case, in which Rakesh Ranjan Yadav alias Rocky Yadav, the son of now suspended JD (U) MLC Manorama Devi, is an accused.
"So LJP demands President's rule in Bihar and a CBI investigation into the Aditya murder case," it said.
Also Read
Chirag, who is LJP's Parliamentary Board Chairman, had on Tuesday met Union Home Minister Rajnath Singh and sought imposition of President's rule in Bihar.
Aditya was shot dead last week allegedly by Rocky for overtaking his vehicle, triggering widespread shock and outrage and giving fresh ammunition to the Opposition to attack the Nitish government.
The accused was arrested a few days back.